I've always thought of maths as the subject that really sorts the clever-clogs from the rest, but there can be other tests. Law and logic is one - I sometimes read the Times law reports and find I'm lost in a maze of conditional clauses, can't tell what they're saying, and have to go to the first or last lines to find out who won - and even then I don't know why. OK, I might be able to work it out by making notes, but I can't hold all the logic in my head.

When I first learned programming we did Assembler, which IIRC is as low-level a language as you get before you have to start worrying about what hardware you're writing for. One of our exercises was a simple task - read a file, print the contents to a page, keep a linecount for the new page, print a pagecount on each page. It took me about a page and a bit of code, written on a coding form - you didn't actually get to see a keyboard back then, as the training section also trained data entry staff, and they typed the code in. Most of the people in the class wrote a similar amount.

One guy wrote it in 6 or 7 lines of code - and it worked. We looked at his code and how he was using the registers - and we could then see how it worked. What none of us could understand was how he'd seen that way of doing it, which was so obvious to him. His brain worked on a different level.

At another level, Microsoft cofounder Paul Allen on recognising when you're in the wrong intellectual league :

I was decent in math, and Bill (Gates) was brilliant, but by then I spoke from my experience at Washington State. One day I watched a professor cover the blackboard with a maze of partial differential equations, and they might as well have been hieroglyphics from the Second Dynasty. It was one of those moments when you realize, I just can’t see it. I felt a little sad, but I accepted my limitations. I was O.K. with being a generalist.

For Bill it was different. When I saw him again over Christmas break, he seemed subdued. I asked him about his first semester, and he said glumly, “I have a math professor who got his Ph.D. at 16.” The course was purely theoretical, and the homework load ranged up to 30 hours a week. Bill put everything into it and got a B. When it came to higher mathematics, he might have been one in a hundred thousand students or better. But there were people who were one in a million or one in 10 million, and some of them wound up at Harvard. Bill would never be the smartest guy in that room, and I think that hurt his motivation. He eventually switched his major to applied math.